Research

I am broadly interested in algorithms and lower bounds. I
particularly focus on really efficient algorithms — as
inputs get larger, even quadratic algorithms are typically too slow.
We would like our algorithms to take nearly linear or
even sublinear time and space.

Sublinear algorithms are tricky, though — you can't even read
or store the whole input. Much of my research has focused
on compressive sensing and sparse recovery, where you
want to estimate a vector from a small linear "sketch" of it. One
important subtopic is sparse Fourier transforms, where we
showed how to estimate the Fourier transform in less time than the FFT
for sparse data.

Another aspect of my research is lower bounds. For many of
the above problems and other statistical problems, we can achieve
matching (or nearly matching) lower bounds on the sample complexity
or space complexity. This lets us know when to stop looking for
better algorithms, and to instead look for better problems.